Water Resources Research

A simple analytic model is proposed which predicts the unsaturated hydraulic conductivity curves by using the moisture content‐capillary head curve and the measured value of the hydraulic conductivity at saturation. It is similar to the Childs and Collis‐George (1950) model but uses a modified assumption concerning the hydraulic conductivity of the pore sequence in order to take into account the effect of the larger pore section. A computational method is derived for the determination of the residual water content and for the extrapolation of the water content‐capillary head curve as measured in a limited range. The proposed model is compared with the existing practical models of Averjanov (1950), Wyllie and Gardner (1958), and Millington and Quirk (1961) on the basis of the measured data of 45 soils. It seems that the new model is in better agreement with observations.

Correlation and correlation‐based measures (e.g., the coefficient of determination) have been widely used to evaluate the “goodness‐of‐fit” of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values (outliers) and are insensitive to additive and proportional differences between model predictions and observations. Because of these limitations, correlation‐based measures can indicate that a model is a good predictor, even when it is not. In this paper, useful alternative goodness‐of‐fit or relative error measures (including the coefficient of efficiency and the index of agreement) that overcome many of the limitations of correlation‐based measures are discussed. Modifications to these statistics to aid in interpretation are presented. It is concluded that correlation and correlation‐based measures should not be used to assess the goodness‐of‐fit of a hydrologic or hydroclimatic model and that additional evaluation measures (such as summary statistics and absolute error measures) should supplement model evaluation tools.

The successful application of a conceptual rainfall‐runoff (CRR) model depends on how well it is calibrated. Despite the popularity of CRR models, reports in the literature indicate that it is typically difficult, if not impossible, to obtain unique optimal values for their parameters using automatic calibration methods. Unless the best set of parameters associated with a given calibration data set can be found, it is difficult to determine how sensitive the parameter estimates (and hence the model forecasts) are to factors such as input and output data error, model error, quantity and quality of data, objective function used, and so on. Results are presented that establish clearly the nature of the multiple optima problem for the research CRR model SIXPAR. These results suggest that the CRR model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets. Next, the performance of three existing global search procedures are evaluated on the model SIXPAR. Finally, a powerful new global optimization procedure is presented, entitled the shuffled complex evolution (SCE‐UA) method, which was able to consistently locate the global optimum of the SIXPAR model, and appears to be capable of efficiently and effectively solving the CRR model optimization problem.

Some of the characteristics that complicate the analysis of water quality time series are non‐normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow‐adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow‐adjusted concentrations, which may also be seasonal and non‐normal, can then be tested for trend by using the seasonal Kendall test.

The soil moisture characteristic may be modeled as a power curve combined with a short parabolic section near saturation to represent gradual air entry. This two‐part function—together with a power function relating soil moisture and hydraulic conductivity—is used to derive a formula for the wetting front suction required by the Green‐Ampt equation. Representative parameters for the moisture characteristic, the wetting front suction, and the sorptivity, a parameter in the infiltration equation derived by Philip (1957), are computed by using the desorption data of Holtan et al. (1968). Average values of the parameters, and associated standard deviations, are calculated for 11 soil textural classes. The results of this study indicate that the exponent of the moisture characteristic power curve can be predicted reasonably well from soil texture and that gradual air entry may have a considerable effect on a soil's wetting front suction.

It is now well established that forested catchments have higher evapotranspiration than grassed catchments. Thus land use management and rehabilitation strategies will have an impact on catchment water balance and hence water yield and groundwater recharge. The key controls on evapotranspiration are rainfall interception, net radiation, advection, turbulent transport, leaf area, and plant‐available water capacity. The relative importance of these factors depends on climate, soil, and vegetation conditions. Results from over 250 catchments worldwide show that for a given forest cover, there is a good relationship between long‐term average evapotranspiration and rainfall. From these observations and on the basis of previous theoretical work a simple two‐parameter model was developed that relates mean annual evapotranspiration to rainfall, potential evapotranspiration, and plant‐available water capacity. The mean absolute error between modeled and measured evapotranspiration was 42 mm or 6.0%; the least squares line through the origin had as lope of 1.00 and a correlation coefficient of 0.96. The model showed potential for a variety of applications including water yield modeling and recharge estimation. The model is a practical tool that can be readily used for assessing the long‐term average effect of vegetation changes on catchment evapotranspiration and is scientifically justifiable.

A model is presented for calculating the daily evaporation rate from a crop surface. It applies to a row crop canopy situation in which the soil water supply to the plant roots is not limited and the crop has not come into an advanced stage of maturation or senescence. The crop evaporation rate is calculated by adding the soil surface and plant surface components (each of these requiring daily numbers for the leaf area index), the potential evaporation, the rainfall, and the net radiation above the canopy. The evaporation from the soil surface E_s is calculated in two stages: (1) the constant rate stage in which E_s is limited only by the supply of energy to the surface and (2) the falling rate stage in which water movement to the evaporating sites near the surface is controlled by the hydraulic properties of the soil. The evaporation from the plant surfaces E_p is predicted by using an empirical relation based on local data, which shows how E_p is related to E_o through the leaf area index. The model was used to obtain the total evaporation rate E = E_s + E_p of a developing grain sorghum (Sorghum bicolor L.) canopy in central Texas. The results agreed well with values for E measured directly with a weighing lysimeter.

Canopy temperatures, obtained by infrared thermometry, along with wet‐ and dry‐bulb air temperatures and an estimate of net radiation were used in equations derived from energy balance considerations to calculate a crop water stress index (CWSI). Theoretical limits were developed for the canopy air temperature difference as related to the air vapor pressure deficit. The CWSI was shown to be equal to 1 ‐ E/E_p, the ratio of actual to potential evapotranspiration obtained from the Penman‐Monteith equation. Four experimental plots, planted to wheat, received postemergence irrigations at different times to create different degrees of water stress. Pertinent variables were measured between 1340 and 1400 each day (except some weekends). The CWSI, plotted as a function of time, closely paralleled a plot of the extractable soil water in the 0‐ to 1.1‐m zone. The usefulness and limitations of the index are discussed.

Landsliding in response to rainfall involves physical processes that operate on disparate timescales. Relationships between these timescales guide development of a mathematical model that uses reduced forms of Richards equation to evaluate effects of rainfall infiltration on landslide occurrence, timing, depth, and acceleration in diverse situations. The longest pertinent timescale is A/D₀, where D₀ is the maximum hydraulic diffusivity of the soil and A is the catchment area that potentially affects groundwater pressures at a prospective landslide slip surface location with areal coordinates x, y and depth H. Times greater than A/D₀ are necessary for establishment of steady background water pressures that develop at (x, y, H) in response to rainfall averaged over periods that commonly range from days to many decades. These steady groundwater pressures influence the propensity for landsliding at (x, y, H), but they do not trigger slope failure. Failure results from rainfall over a typically shorter timescale H²/D₀ associated with transient pore pressure transmission during and following storms. Commonly, this timescale ranges from minutes to months. The shortest timescale affecting landslide responses to rainfall is , where g is the magnitude of gravitational acceleration. Postfailure landslide motion occurs on this timescale, which indicates that the thinnest landslides accelerate most quickly if all other factors are constant. Effects of hydrologic processes on landslide processes across these diverse timescales are encapsulated by a response function, , which depends only on normalized time, t*. Use of R(t*) in conjunction with topographic data, rainfall intensity and duration information, an infinite‐slope failure criterion, and Newton's second law predicts the timing, depth, and acceleration of rainfall‐triggered landslides. Data from contrasting landslides that exhibit rapid, shallow motion and slow, deep‐seated motion corroborate these predictions.

The dispersive mixing resulting from complex flow in three‐dimensionally heterogeneous porous media is analyzed using stochastic continuum theory. Stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three‐dimensional, statistically anisotropic input covariance describing the hydraulic conductivity. With a statistically isotropic input covariance, the longitudinal macrodispersivity is convectively controlled, but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term. With an arbitrarily oriented anisotropic conductivity covariance, all components of the macrodispersivity tensor are convectively controlled, and the ratio of transverse to longitudinal dispersivity is of the order of 10⁻¹. In this case the off‐diagonal components of the dispersivity tensor are significant, being numerically larger than the diagonal transverse terms, and the transverse dispersion process can be highly anisotropic. Dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and Monte Carlo simulations. The theory, which treats the asymptotic condition of large displacement, indicates that a classical gradient transport (Fickian) relationship is valid for large‐scale displacements.